# EC GATE 2011 (Test 1)

Tag: ec gate 2011
Q.1
Choose the word from the options given below that is most nearly opposite in meaning to the given word: Frequency
A. periodicity
B. rarity
D. persistency
Explaination / Solution:

Periodicity is almost similar to frequency. Gradualness means something happening with time. Persistency is endurance. Rarity is opposite to frequency

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Topic: Arithmetic Tag: EC GATE 2011
Q.2
There are two candidates P and Q in an election. During the campaign, 40% of the voters promised to vote for P, and rest for Q. However, on the day of election 15% of the voters went back on their promise to vote for P and instead voted forQ. 25% of the voters went back on their promise to vote for Q and instead voted for P. Suppose, P lost by 2 votes, then what was the total number of voters?
A. 100
B. 110
C. 90
D. 95
Explaination / Solution:
No Explaination.

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Q.3
The output of a 3-stage Johnson (twisted ring) counter is fed to a digital-to analog (D/A) converter as shown in the figure below. Assume all the states of the counter to be unset initially. The waveform which represents the D/A converter output v0 is

A.
B.
C.
D.
Explaination / Solution:

All the states of the counter are initially unset.

State Initially are shown below in table:
Q2Q1Q0
0  0  0  0
1  0  0  4
1  1  0  6
1  1  1  7
0  1  1  3
0  0  1  1
0  0  0  0

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Q.4
In the circuit shown below, capacitors C1 and C2 are very large and are shorts at the input frequency. vi is a small signal input. The gain magnitude  at 10 M rad/s is

A. maximum
B. minimum
C. unity
D. zero
Explaination / Solution:

For the parallel RLC circuit resonance frequency is,

Thus given frequency is resonance frequency and parallel RLC circuit has maximum impedance at resonance frequency
Gain of the amplifier is   where ZC is impedance of parallel RLC circuit.

Hence at this frequency (ωr), gain is
which is maximum
Therefore gain is maximum at ωr = 10 /sec M rad .

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Q.5
For a BJT the common base current gain α = 0.98 and the collector base junction reverse bias saturation current ICO = 0.6 μA. This BJT is connected in the common emitter mode and operated in the active region with a base drive current IB = 204 A. The collector current IC for this mode of operation is
A. 0.98 mA
B. 0.99 mA
C. 1.0 mA
D. 1.01 mA
Explaination / Solution:

In active region, for common emitter amplifier,

Substituting ICO = 0.6 μA and IB = 204 μA in above eq we have,
IC = 1.01 mA

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Q.6

The ac output voltage Vac is
A. 0.25 cos (𝜔t) mV
B. 1 cos (𝜔t) mV
C. 2 cos (𝜔t) mV
D. 22 cos (𝜔t) mV
Explaination / Solution:

The forward resistance of each diode is

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Q.7
x(t) is a stationary random process with auto-correlation function.   This process is passed through the system shown below. The power spectral density of the output process y(t) is

A. (4π2f2 + 1) exp (-πf2)
B. (4π2f2 - 1) exp (-πf2)
C. (4π2f2 + 1) exp (-πf)
D. (4π2f2 - 1) exp (-πf)
Explaination / Solution:

The given circuit can be simplified as

Power spectral density of output is

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Q.8
An analog signal is band-limited to 4 kHz, sampled at the Nyquist rate and the samples are quantized into 4 levels. The quantized levels are assumed to be independent and equally probable. If we transmit two quantized samples per second, the information rate is ________ bits / second.
A. 1
B. 2
C. 3
D. 4
Explaination / Solution:

Quantized 4 level require 2 bit representation i.e. for one sample 2 bit are required. Since 2 sample per second are transmitted we require 4 bit to be transmitted per second.

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Q.9
The input-output transfer function of a plant  The plant is placed in a unity negative feedback configuration as shown in the figure below.
The gain margin of the system under closed loop unity negative feedback is

A. 0 dB
B. 20 dB
C. 26 dB
D. 46 dB
Explaination / Solution:

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Q.10
Consider the following statements regarding the complex Poynting vector  for the power radiated by a point source in an infinite homogeneous and lossless medium. Re() denotes the real part of  denotes a spherical surface whose centre is at the point source, and denotes the unit surface normal on S. Which of the following statements is TRUE?
A. Re() remains constant at any radial distance from the source
B.  Re() increases with increasing radial distance from the source
C.   remains constant at any radial distance from the source
D.   decreases with increasing radial distance form the source